Multiple choice

Volume and total surface area of a solid hemisphere are equal in magnitude. The volume is expressed in cm$^3$ and the area is expressed in cm$^2$. Find the radius of hemisphere.

  1. $3$ cm
  2. $4$ cm
  3. $4.5$ cm
  4. $5.5$ cm
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C Correct answer
Explanation

Volume of hemisphere = 2/3 * pi * r^3. Total surface area = 3 * pi * r^2. 2/3 * pi * r^3 = 3 * pi * r^2. 2/3 * r = 3. r = 9/2 = 4.5 cm.

AI explanation

Equating the hemisphere volume formula, two thirds times pi times r cubed, to the total surface area formula, three times pi times r squared, gives two thirds times r equals 3. Solving this linear equation for the radius yields r equals 4.5 cm.

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